Julesz (1975) famously conjectured that any two textures with identical autocorrelation functions would be indiscriminable. Although various counterexamples have been discovered, new methods for constructing textures with identical space-average autocorrelation functions remain important because they often lead to useful insights about preattentive visual processing.

We describe a new method that uses three simple facts in concert to generate texture pairs with equal space-average autocorrelation functions. First, if an image is shifted, its autocorrelation function remains unchanged. Second, if an image is rotated 180 degrees, its autocorrelation function remains unchanged. Third, for any two random stimuli, at least one of which has expectation 0 (i.e., expectation equal to the uniform background field), the expectation of the autocorrelation function of their sum is equal to the sum of the expectations of their separate autocorrelation functions.

How do we use these facts to make textures? Start, for example, with two small figures, A and B (e.g., an ‘L’ shape and a rectangle), configured in some way on a gray background. Fix the contrast of figure A (e.g., make A white), but let B be white or black with equal probability: call this type of micropattern M1. Then translate and/or rotate by 180 deg.either or both of A and/or B to form a new micropattern type, M2. Tile the left side of the stimulus field with independent realizations of M1 and the right side with realizations of M2.

This method often yields powerfully distinct texture pairs. Discriminability is harder to achieve if one requires that M1 and M2 “share the same footprint” (i.e., |M1| = |M2|). We will demonstrate several discriminable textures satisfying this constraint.